Tips:
Take pitches against Mariano Rivera. Remember, he's a relief pitcher. His stamina is going to start to get brutally low once he hits about 40 pitches. Just survive with enough outs until then and I promise you'll beat him.
Remember to look at each challenge AND THEN set your Perks. For example, if it says you're starting in the 8th inning, you know to use a perk like Spark-Plug where you make better contact in and after the 7th inning. This will save your life.
Personally, I always switch to Directional for Showdowns. It makes it 100x easier for me, for some reason.
Don't draft more than one reliever and starter. I didn't even use my starting pitcher but maybe you will. I'm not certain that they have more challenges.
In my experiences, I've had the most success with the Defibrillator perks; silver gives you a contact boost in even counts (0-0, 1-1, 2-2); gold gives you a contact boost when you are behind in the count (love this one); and the diamond gives you a huge contact boost when you have two strikes. The diamond one is great for a number of reasons, not only can you basically put the controller down until you have 2 strikes but once you do, you can pretty much foul ANYTHING off which is going to raise the pitch count even higher!
I'm also a big fan of the perks that affect exit velocity. In combination with ones that give you a contact boost, you can straight wreck these final bosses.